The Supreme Court's first case was selected for its importance to the public
The first hearing in the new UK Supreme Court is a challenge to government powers to create laws without a vote in Parliament, it has been argued.
Five men suspected of financing terrorism claim a Treasury freeze on their assets breaches their rights.
Tim Owen QC said the case involved "fundamental constitutional issues" about ministers making laws without parliamentary debate or scrutiny.
The court allowed one of the defendants to be named as Mohammed al Ghabra.
Mr Owen, representing three of the men, said the government had imposed "a draconian, intrusive regime which destroys the individual's power to live any sort of normal life without any conviction in a court".
"It is an abuse of executive power," he said.
The five suspects, four of whom cannot be named, have not been convicted of funding terrorism.
FROM INSIDE COURT ONE
Daniel Sandford, home affairs correspondent, BBC News
We have started on time at eleven o'clock sharp.
The court is packed in a way no Law Lords hearings had been since the days of the General Pinochet case. All the lawyers have the nervous excitement of children on their first day at school.
Grandees including the Duke of Wellington stare down from the portraits on the Portland stone walls below the hammer beam roof.
The room has the feel of a medieval banqueting hall, but what is taking place here is a modern legal milestone. It is the first time that the UK's final court of appeal has heard a case outside Parliament.
It is very different for the media too. We are allowed to use laptops and PDAs (including the one I am writing on now.) Small TV cameras sit discreetly in the four corners of the room. Almost everything that happens here today (barring anything particularly sensitive) is available to be broadcast.
But the Treasury has blocked access to their bank accounts, welfare benefits and other assets.
They are allowed a small amount of money for basic expenses, must account for their expenditure, and anyone providing them with "an economic resource" is liable to face criminal proceedings.
Ministers argue these powers were legitimised by adopting UN Security Council resolutions intended to tackle global terrorism.
The asset-freezing powers were introduced in 2006 - but were never scrutinised or approved by Parliament, which the men's lawyers say is unlawful.
Mr Owen said the lawfulness of the restrictions depended on analysis of the United Nations Act and UK powers allowing such measures through an Order in Council.
"It was not intended to be an enormous, unlimited delegation of the legislative power by Parliament," Mr Owen said.
"Parliament did not deliver a blank cheque to the executive."
This was the first time the courts had had a chance to consider these questions, he said.
The Supreme Court has taken over from the Law Lords as the final court of appeal for UK civil cases and criminal cases in England, Wales and Northern Ireland.
The £59m court is based at Middlesex Guildhall in central London.
Its creation was intended to make the judiciary independent of Parliament by ending the House of Lords' judicial role.
The casework that will be dealt with by the Supreme Court is exactly the same as that which came before the justices in the Lords.
It will deal only with cases that the justices consider to be the most important and where rulings have far-reaching implications.
The first case was chosen as it deals with human rights and anti-terrorism powers.